Answer:
to make sure you understand the question
Step-by-step explanation:
Answer:
1/2
Step-by-step explanation:
Since it is given that the cone and the hemisphere have the same height, and since the height of a hemisphere would be equal to its radius, the cones height must also be equal to its base radius.
With this information we can use the respective volume formulas.
Hemisphere:
πr^3
Cone:
πhr^2
Since h (height) = r we can say the cone volume equals:
πr^3
Now to find the ratio we divide the cone volume equation by the hemisphere volume equation
pi and r^3 cancels out from the division and we are left with
ratio = (1/3)/(2/3)
ratio = 1/2
Answer:

Step-by-step explanation:
Assuming this problem :"Only 30% of the students in a certain liberal arts college are males.
If two students from this college are selected at random, what is the probability that they are both males?"
Previous concepts
An independent event is an "event that has no connection to another event's chances of happening ". For this case we can assume that if one person is male and if we select another one the probability that this one would be male or female is totally indepedent from the first selection.
When we have two independent events let's say A and B and we want to find the probability that both events occurs at the same time we can use the following formula:

Solution to the problem
We can define some notation:
first person selected is a male
second person selected is male
On this case we want the probability that both would be males. And we can express this like this on math terms:

For this case we can assume that the two events are independent. And in order to find the probability for two events independents events we just need to multiply the probabilities of each one like this:

Answer:
-6
Step-by-step explanation:
We know that since Ax + By = 3 passes through (-7, 2), then if we plug -7 in for x and 2 in for y, the equation is satisfied. So, let's do that:
Ax + By = 3
A * (-7) + B * 2 = 3
-7A + 2B = 3
We also know that this line is parallel to x + 3y = -5, which means their slopes are the same. Let's solve for y in the second equation:
x + 3y = -5
3y = -x - 5
y = (-1/3)x - (5/3)
So, the slope of this line is -1/3, which means the slope of Ax + By = 3 is also -1/3. Let's solve for y in the first equation:
Ax + By = 3
By = -Ax + 3
y = (-A/B)x + 3/B
This means that -A/B = -1/3. So, we have a relationship between A and B:
-A/B = -1/3
A/B = 1/3
B = 3A
Plug 3A in for B into the equation we had where -7A + 2B = 3:
-7A + 2B = 3
-7A + 2 * 3A = 3
-7A + 6A = 3
-A = 3
A = -3
Use this to solve for B:
B = 3A
B = 3 * (-3) = -9
So, B = -9 and A = -3. Then B - A is:
B - A = -9 - (-3) = -9 + 3 = -6
The answer is -6.
<em>~ an aesthetics lover</em>
Answer:
Hey there!
You can think of the rate of change as the slope of a quadratic function- here we see that it is 9/-3, or - 3.
Let me know if this helps :)